Given that the new equation for cost is y= 3300+ 55x, explain why the equation for money earned is now given by y = 1800 + 60x (where x is the number of jeans sold after the first 60)

Let's break down the given equations and the reasoning behind the change in the equation for money earned.

### Equation for Cost:
The equation for cost is given by:
\[ y = 3300 + 55x \]
- **3300**: This is the fixed cost (perhaps related to starting or operational costs that don't depend on the number of jeans produced).
- **55**: This is the variable cost per unit, meaning that for each additional pair of jeans made, it costs an additional \$55.
- **x**: This is the number of jeans produced.

### Equation for Money Earned:
The equation for money earned is now:
\[ y = 1800 + 60x \]
- **1800**: This is a fixed amount of money earned, possibly from sales of the first 60 jeans.
- **60**: This is the money earned per jean after the first 60 jeans are sold.
- **x**: This represents the number of jeans sold **after** the first 60.

### Why is the equation for money earned in this form?
This equation suggests that the first 60 jeans have already been accounted for in some way, either through fixed contracts or some sort of bulk sale, generating an initial fixed income of \$1800. The money earned after this point grows at a rate of \$60 for each additional jean sold.

This could be interpreted as:
1. **Initial sales (first 60 jeans)**: The first 60 jeans contribute to the initial earnings, possibly sold at a different rate or considered part of a bulk deal. This is captured by the \$1800.
2. **Additional sales**: For jeans sold **after** the first 60, the money earned per additional jean is \$60 (perhaps indicating a higher selling price, discount, or deal for larger quantities sold).

The shift in the equation implies that the pricing structure changes after a certain volume of sales, possibly due to discounts or pricing strategies.

### In summary:
- The **fixed amount** of \$1800 represents earnings from the first 60 jeans.
- For jeans sold beyond this initial batch, you earn \$60 per jean.
- The **60** in the second equation could indicate a shift in the earnings model or represent jeans sold at a premium after hitting a threshold.

Would you like further clarification or more details on this reasoning?

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Here are 5 questions to expand on this information:
1. What factors could influence the variable cost per jean?
2. How would the equations change if the fixed costs increase?
3. What could cause the money earned per jean to be \$60 instead of \$55?
4. How would profits be calculated using these two equations?
5. What happens to the break-even point if the cost structure changes?

**Tip**: Always look at both fixed and variable components in equations to understand how they influence the total cost or earnings.

Given that the new equation for cost is y = 3300 + 55x, explain why the equation for money earned is now given by y = 1800 + 60x (where x is the number of jeans sold after the first 60)

Explore how to analyze cost and earnings with the linear equations y = 3300 + 55x and y = 1800 + 60x, where x represents jeans sold after the first 60. Learn key algebraic concepts like fixed and variable costs, and discover how profit structures change with sales volume. Suitable for high school students.

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